How to Add Fractions

Before learning how to add fractions, make sure you first truly understand fractions. Please visit the rules of fractions main pageif necessary.  Also, you might get hungry during this lesson, so feel free to order pizza now.

Adding fractions is easy when the pieces are the same size.  For example...

Because the pieces are the same size, it is fair to say that...
1 piece + 1 piece = 2 pieces.  We now know how many pieces we have (top/numerator), we just need to know the total number of pieces that our pizza was cut into (bottom/denominator).

Adding fractions gets more difficult when the pieces are different sizes.  For example...

Because the pieces are different sizes, it is not fair to say that we have 2 pieces this time.  Wouldn't you rather have these 2 pieces than the 2 pieces above? 

To add fractions, we must first make the pieces the same size!  Take a look at how we made that second, bigger piece into 2 smaller pieces so that all the slices are equal...

Because we made the pieces the same size (like in the first example) we can simply add them up.  1 piece + 2 pieces = 3 pieces.

How to Add Fractions - The #1 Rule

You MUST have all the pieces the same size before you add them.  If they are not the same size, make them the same size!  If your pieces are not the same size, then somebody is getting ripped off (especially if you are dealing with money instead of pizza)!

For more information on how to "make pieces the same size," please view our equivalent fractions page and then practice the skill with our equivalent fractions worksheets.

Determining the Number of Pieces

Here is our original pizza, before and after we sliced it up.  The pizza was sliced into 8 equal pieces.

*Remember, the total number of pieces is the denominator (bottom) of the fraction.  The number of pieces that you have is the numerator (top) of the fraction.

Case #1:  Same Denominators

If the denominators are the same, then your answer will have that same denominator as well!  Just add up the two numerators.

Example #1:    1/8 + 1/8 = 2/8

Example #2:    1/8 + 2/8 = 3/8

Case #2:  Different (Unlike) Denominators

If the denominators are different, then you must first change the entire fraction into a fraction with the same denominator.  Consult our equivalent fractions page for me help on how to do this.

Example #1:    1/8 + 2/4 --> change to 1/8 + 4/8 = 5/8

Example #2:    1/2 + 2/8 --> change to 4/8 + 2/8 = 6/8